An EM Algorithm for Estimating Equations

Elashoff, M; Ryan, L

An EM Algorithm for Estimating Equations

Elashoff, M Ryan, L

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Publication Type:: Journal Article
Citation:: Journal of Computational and Graphical Statistics, 2004, 13 (1), pp. 48 - 65
Issue Date:: 2004-03-01

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Field	Value	Language
dc.contributor.author	Elashoff, M	en_US
dc.contributor.author	Ryan, L https://orcid.org/0000-0001-5957-2490	en_US
dc.date.issued	2004-03-01	en_US
dc.identifier.citation	Journal of Computational and Graphical Statistics, 2004, 13 (1), pp. 48 - 65	en_US
dc.identifier.issn	1061-8600	en_US
dc.identifier.uri	http://hdl.handle.net/10453/26176
dc.description.abstract	This article presents an algorithm for accommodating missing data in situations where a natural set of estimating equations exists for the complete data setting. The complete data estimating equations can correspond to the score functions from a standard, partial, or quasi-likelihood, or they can be generalized estimating equations (GEEs). In analogy to the EM, which is a special case, the method is called the ES algorithm, because it iterates between an E-Step wherein functions of the complete data are replaced by their expected values, and an S-Step where these expected values are substituted into the complete-data estimating equation, which is then solved. Convergence properties of the algorithm are established by appealing to general theory for iterative solutions to nonlinear equations. In particular, the ES algorithm (and indeed the EM) are shown to correspond to examples of nonlinear Gauss-Seidel algorithms. An added advantage of the approach is that it yields a computationally simple method for estimating the variance of the resulting parameter estimates.	en_US
dc.relation.ispartof	Journal of Computational and Graphical Statistics	en_US
dc.relation.isbasedon	10.1198/1061860043092	en_US
dc.subject.classification	Statistics & Probability	en_US
dc.title	An EM Algorithm for Estimating Equations	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	13	en_US
utslib.for	010401 Applied Statistics	en_US
utslib.for	0104 Statistics	en_US
utslib.for	1403 Econometrics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	closed_access
pubs.issue	1	en_US
pubs.publication-status	Published	en_US
pubs.volume	13	en_US

Abstract:

This article presents an algorithm for accommodating missing data in situations where a natural set of estimating equations exists for the complete data setting. The complete data estimating equations can correspond to the score functions from a standard, partial, or quasi-likelihood, or they can be generalized estimating equations (GEEs). In analogy to the EM, which is a special case, the method is called the ES algorithm, because it iterates between an E-Step wherein functions of the complete data are replaced by their expected values, and an S-Step where these expected values are substituted into the complete-data estimating equation, which is then solved. Convergence properties of the algorithm are established by appealing to general theory for iterative solutions to nonlinear equations. In particular, the ES algorithm (and indeed the EM) are shown to correspond to examples of nonlinear Gauss-Seidel algorithms. An added advantage of the approach is that it yields a computationally simple method for estimating the variance of the resulting parameter estimates.

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http://hdl.handle.net/10453/26176